A new method is developed for integer ambiguity resolution in carrier-phase differential GPS (CDGPS) positioning. The method is novel in that it is (1) data-driven, (2) generalized to include partial ambiguity resolution, and (3) amenable to a full characterization of the prior and posterior distributions of the three-dimensional baseline vector that results from CDGPS. The technique is termed generalized integer aperture bootstrapping (GIAB). GIAB improves the availability of integer ambiguity resolution for high-integrity, safety-critical systems. Current high-integrity CDGPS algorithms, such as EPIC and GERAFS, evaluate the prior risk of position domain biases due to incorrect integer ambiguity resolution without further validation of the chosen solution. This model-driven approach introduces conservatism which tends to reduce solution availability. Common data-driven ambiguity validation methods, such as the ratio test, control the risk of incorrect ambiguity resolution by shrinking an integer aperture (IA), or acceptance region. The incorrect fixing risk of current IA methods is determined by functional approximations that are inappropriate for use in safety-of-life applications. Moreover, generalized IA (GIA) methods incorrectly assume that the baseline resulting from partial ambiguity resolution is zero mean. Each of these limitations is addressed by GIAB, and the claimed improvements are validated by Monte Carlo simulation. The performance of GIAB is then optimized by tuning the integer aperture size to maximize the prior probability of full ambiguity resolution. GIAB is shown to provide higher availability than EPIC for the same integrity requirements.